4(1/5x-1)=2/3x+17

Solution for 4(1/5x-1)=2/3x+17 equation:

4(1/5x-1)=2/3x+17

We move all terms to the left:

4(1/5x-1)-(2/3x+17)=0


Domain of the equation: 5x-1)!=0

x∈R



Domain of the equation: 3x+17)!=0

x∈R


We multiply parentheses

4x-(2/3x+17)-4=0

We get rid of parentheses

4x-2/3x-17-4=0

We multiply all the terms by the denominator


4x*3x-17*3x-4*3x-2=0

Wy multiply elements

12x^2-51x-12x-2=0

We add all the numbers together, and all the variables

12x^2-63x-2=0

a = 12; b = -63; c = -2;
Δ = b2-4ac
Δ = -632-4·12·(-2)
Δ = 4065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{4065}}{2*12}=\frac{63-\sqrt{4065}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4065}}{2*12}=\frac{63+\sqrt{4065}}{24}
$